A classification of unipotent spherical conjugacy classes in bad characteristic

TL;DR

This paper classifies unipotent conjugacy classes in simple algebraic groups over fields with bad characteristic and explores the sphericity of fixed point subgroups under involutions, revealing new structural insights.

Contribution

It provides a complete classification of spherical unipotent conjugacy classes in bad characteristic and analyzes the sphericity of fixed point subgroups under involutions.

Findings

Classification of spherical unipotent conjugacy classes in bad characteristic

Fixed point subgroups of involutions are spherical when characteristic is 2

Structural insights into algebraic groups in bad characteristic

Abstract

Let G be a simple algebraic group over an algebraically closed field k of bad characteristic. We classify the spherical unipotent conjugacy classes of G. We also show that if the characteristic of k is 2, then the fixed point subgroup of every involutorial automorphism (involution) of G is a spherical subgroup of G.